1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The centroid of tetrahedron with vertices $\mathrm{P}(5,-7,0), \mathrm{Q}(\mathrm{a}, 5,3), \mathrm{R}(4,-6, b)$ and $\mathrm{S}(6, \mathrm{c}, 2)$ is $(4,-3,2)$, then the value of $2 a+3 b+c$ is equal to

A
15
B
$-$7
C
7
D
$-$5
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A variable plane passes through the fixed point $(3,2,1)$ and meets $X, Y$ and $Z$ axes at points $A$, B and C respectively. A plane is drawn parallel to YZ - plane through A , a second plane is drawn parallel to ZX -plan through B , a third plane is drawn parallel to XY - plane through C . Then locus of the point of intersection of these three planes, is

A
  $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{11}{6}$
B
$\frac{x}{3}+\frac{y}{2}+\frac{z}{1}=1$
C
$\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$
D
$x+y+z=6$
3
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=\mathrm{z}$ is __________ units.

A
$3 \sqrt{10}$
B
$10 \sqrt{3}$
C
$\frac{10}{\sqrt{3}}$
D
$\frac{20}{3}$
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If for some $\alpha \in \mathbb{R}$, the lines $\mathrm{L}_1: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\mathrm{L}_2: \frac{x+2}{\alpha}=\frac{y+1}{5-\alpha}=\frac{z+1}{1}$ are coplanar, then the line $L_2$ passes through the point

A
$(10,2,2)$
B
$(2,-10,-2)$
C
$(10,-2,-2)$
D
$(-2,10,2)$
MHT CET Subjects
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